Trump said the two had also talked about trade, and his only public comment on the discussion was a tweet.
The new emperor was presented with the items his father Akihito relinquished a day earlier: sacred imperial treasures of a sword and a jewel, as well as the seal of state.
He also visited a soccer facility called J-Village, which temporarily served as a place for workers dealing with the plant accident.
However, Abe claimed that Trump has worked bravely in resolving the nuclear problem and missiles from North Korea.
TPP is open for all countries that are willing to share its ideas, Japanese Prime Minister Shinzo Abe said at the first ministerial meeting of the TPP commission in Tokyo.
The US president added that the trade deficit between Japan and the United States is quite significant, but it is going down.
The annual meeting is being attended by leaders of the top 20 economies of the world.
Tokyo is also considering upgrading its helicopter carriers so that they can transport and launch fighter jets, local news agency reported.
The two countries are still technically at war, with neither side historically prepared to budge on a row over the ownership of the islands seized by Russia in the closing days of the conflict.
The two leaders met face-to-face on the sidelines of the regional Association of Southeast Asian Nations (ASEAN) summit in Singapore.
Speaking after talks with Japanese Prime Minister Shinzo Abe, he reiterated Washington's position that US businesses have faced unfair obstacles in Japan.
Modi, who arrived in Japan on Saturday to attend the 13th India-Japan annual summit, detailed India's economic and technological growth during his four-year tenure.
Modi gifted Abe with two handcrafted stone bowls and dhurries made from rose quartz and yellow quartz stone sourced from Rajasthan, and a Jodhpuri wooden chest from Rajasthan with traditional work.
PM Modi, who arrived in Tokyo Saturday evening to attend the 13th India-Japan annual summit, has said that his meeting with Abe will add new vigour to the strong friendship between the two countries.
The stone bowls and dhurries were made under the design supervision of the prestigious Ahmedabad-based National Institute of Design.